.TH std::normal_distribution 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::normal_distribution \- std::normal_distribution

.SH Synopsis
   Defined in header <random>
   template< class RealType = double >  \fI(since C++11)\fP
   class normal_distribution;

   Generates random numbers according to the Normal (or Gaussian) random number
   distribution. It is defined as:

   \\(\\small{f(x;\\mu,\\sigma)}=\\frac{1}{\\sigma\\sqrt{2\\pi}
   }\\exp{(-\\frac{1}{2}{(\\frac{x-\\mu}{\\sigma})}^2)}\\)f(x; μ,σ) =

   1
   σ
   √
   2π

   exp⎛
   ⎜
   ⎝

   -1
   2

   ⎛
   ⎜
   ⎝

   x-μ
   σ

   ⎞
   ⎟
   ⎠2
   ⎞
   ⎟
   ⎠

   Here \\(\\small\\mu\\)μ is the Mean and \\(\\small\\sigma\\)σ is the Standard deviation
   (stddev).

   std::normal_distribution satisfies all requirements of RandomNumberDistribution.

.SH Template parameters

   RealType - The result type generated by the generator. The effect is undefined if
              this is not one of float, double, or long double.

.SH Member types

   Member type         Definition
   result_type \fI(C++11)\fP RealType
   param_type \fI(C++11)\fP  the type of the parameter set, see RandomNumberDistribution.

.SH Member functions

   constructor   constructs new distribution
   \fI(C++11)\fP       \fI(public member function)\fP
   reset         resets the internal state of the distribution
   \fI(C++11)\fP       \fI(public member function)\fP
.SH Generation
   operator()    generates the next random number in the distribution
   \fI(C++11)\fP       \fI(public member function)\fP
.SH Characteristics
   mean          returns the distribution parameters
   stddev        \fI(public member function)\fP
   \fI(C++11)\fP
   param         gets or sets the distribution parameter object
   \fI(C++11)\fP       \fI(public member function)\fP
   min           returns the minimum potentially generated value
   \fI(C++11)\fP       \fI(public member function)\fP
   max           returns the maximum potentially generated value
   \fI(C++11)\fP       \fI(public member function)\fP

.SH Non-member functions

   operator==
   operator!=                compares two distribution objects
   \fI(C++11)\fP                   \fI(function)\fP
   \fI(C++11)\fP(removed in C++20)
   operator<<                performs stream input and output on pseudo-random number
   operator>>                distribution
   \fI(C++11)\fP                   \fI(function template)\fP

.SH Example


// Run this code

 #include <cmath>
 #include <iomanip>
 #include <iostream>
 #include <map>
 #include <random>
 #include <string>

 int main()
 {
     std::random_device rd{};
     std::mt19937 gen{rd()};

     // values near the mean are the most likely
     // standard deviation affects the dispersion of generated values from the mean
     std::normal_distribution d{5.0, 2.0};

     // draw a sample from the normal distribution and round it to an integer
     auto random_int = [&d, &gen]{ return std::round(d(gen)); };

     std::map<int, int> hist{};
     for (int n = 0; n != 10000; ++n)
         ++hist[random_int()];

     for (auto [x, y] : hist)
         std::cout << std::setw(2) << x << ' ' << std::string(y / 200, '*') << '\\n';
 }

.SH Possible output:

 -2
 -1
  0
  1 *
  2 ***
  3 ******
  4 ********
  5 **********
  6 ********
  7 *****
  8 ***
  9 *
 10
 11
 12

.SH External links

   1.  Weisstein, Eric W. "Normal Distribution." From MathWorld — A Wolfram Web
       Resource.
   2.  Normal distribution — From Wikipedia.
